You may have to start using timeout for these episodes. Stay as calm as possible and just tell him that he can't be with you if he is going to scream and hit. Sit him in a boring corner where you can keep your eye on him, but don't pay any attention to him. Set a timer that he can see or hear and when the time is up, go and calmly talk to him about why he was in timeout and then give him a hug and let him continue playing. If he gets up from the corner, you just put him back without saying anything. If he's strong willed, this could happen over and over again, but he will eventually get it.
The only other thing you can do is ignore him and stop giving in. If you're at home, let him scream. When he realizes he isn't going to get your attention that way (which is what he is after), he will eventually stop. When he does quit screaming, praise him and talk to him about how he can/should get your attention; by saying "please" and "thank you" and by asking politely for things he wants (this doesn't mean you always have to give them to him though just because he asks nicely). I think it is entirely appropriate to tell him that you don't hit, but that alone may not do the trick. This should be something you say as you're putting him in timeout so that he understands why he is there.
Best of luck to you! This age can be very trying, but it's better to get the upper hand now or he will be ruling the roost by the time he's 4. ;-)